This invention relates to a method and apparatus for generating a phase-adapted coherent secondary radiation in a non-linear crystal by irradiation with a coherent primary radiation, the frequency of the secondary radiation being doubled with respect to the frequency of a primary radiation or changed with respect to the frequencies of two differing primary rays by a sum or difference formation of the primary frequencies.
Coherent secondary radiation may be generated in crystals by utilizing non-linear polarization effects which are caused by the electric fields of an intensive coherent primary radiation, the frequency of the secondary radiation being changed with respect to the frequency of the primary radiation. A laser beam of the frequency f applied to a double-refracting crystal may be effective to generate the harmonic wave of the frequency 2f in the latter. The influence of laser beams of different frequencies, for instance f.sub.1 and f.sub.2, may lead in a non-linear crystal to the generation of the coherent secondary radiation of the sum frequency f.sub.1 + 132 f.sub.2 or of the difference frequency f.sub.1 - f.sub.2. By this generation of secondary radiation the wavelength range of the emission of lasers can be extended. The wavelength range of commercially available dye lasers can be extended by the generation of secondary radiation in a non-linear crystal both to the UV range as also to the IR range. A condition of an effective conversion of a laser radiation acting as primary radiation to a secondary radiation of different frequency is that the primary wave and the secondary wave remain in phase on the irradiation path, i.e., that both waves must have the same phase speed in the non-linear crystal.
For a deduction of the conditions for phase adaption between primary and secondary waves and as pertaining to the prior art, the following explanations are given:
The non-linear interaction between primary and secondary waves is correlated to conditions which take into account the energy and pulse principles.
To maintain the energy and pulse principles the following must apply: EQU f.sub.1 + f.sub.2 = f.sub.3 (I) EQU k.sub.1 + k.sub.2 = k.sub.3 (II)
with EQU .vertline.k.sub.i .vertline.= 2 II f.sub.i (n.sub.i /c)
wherein
f.sub.i = the frequencies,
k.sub.i = the wave vectors,
n.sub.i = n (f.sub.i) the refractive indices for the waves,
c = the light velocity in vacuum.
For a colinear transmission the following condition of phase adaption is obtained therefrom: EQU n.sub.1 f.sub.1 + n.sub.2 f.sub.2 = n.sub.3 f.sub.3 (III)
this can be satisfied in different non-linear crystals in that the dispersion of the light velocity in the crystal is compensated by the anisotropy of the refractive index.
In double-refracting crystals two types of phase adaption are principally possible:
Type 1: The waves of the frequencies f.sub.1 and f.sub.2 have the same polarization (both are either ordinary or extraordinary rays). PA1 Type 2: The polarization directions of the waves of the frequencies f.sub.1 and f.sub.2 are mutually orthogonal (an ordinary and an extraordinary ray). PA1 a. the variation of the laser output frequency: By way of example, this is done by a change in the angular position of the dispersing element in the resonator of the laser; PA1 b. the satisfaction of the condition of phase adaption in the double-refracting crystal: by way of example, this is done by a change in the crystal orientation or in the crystal temperature.
For the specific case of frequency doubling with phase adaption according to type 1 the condition of phase adaption III changes over to EQU n.sub.o (f) = n.sub.e (2f) (IV)
wherein the index o refers to the ordinary ray and the index e refers to the extraordinary ray.
In a uniaxial crystal with negative double refraction the condition (IV) can be satisfied if directions exist in the crystal for which the extraordinary refractive index of the frequency 2f is just as great as the ordinary refractive index for the frequency f. Therefore, if an ordinary polarized wave of the frequency f is passed in this direction through the crystal, then the higher wave generated by the non-linear interaction of the frequency 2f is automatically phase-adapted with extraordinary polarization and can be generated cumulatively on the interaction path.
For a uniaxial crystal with positive double refraction instead of (IV) there is required EQU n.sub.e (f) = n.sub.o (2f) (V)
frequency doubling in uniaxial crystals with phase adaption according to type 2 requires the satisfaction of the conditions EQU n.sub.o (f) + n.sub.e (f) = 2 n.sub.e (2f) (IV') EQU n.sub.o (f) + n.sub.e (f) = 2 n.sub.o (f) (V')
corresponding formulae for the phase adaption in the sum and difference frequency generation can be deducted by analogous reflections and can be gathered from the literature (for instance, J. E. Midwinter, J. Warner, Brit. J. Appl. Phys. 16, 1135 (1965); G. C. Bhar, D. C. Hanna, B. Luther-Davies and R. C. Smith, Optics Communications 6, 323 (1972). The conditions for phase adaption in biaxial crystals can be gathered from Hobden, J. Appl. Phys. 38, 4365 (1967).
If the emission of one or several frequency-variable lasers is used as primary radiation, then by means of non-linear polarization processes in crystals a frequency-variable coherent radiation in the ultra-violet and in the infra-red spectral range can be generated. For generation of tunable and powerful primary radiation dye lasers are available in the visible spectral range. Band width and wavelength of the emitted radiation of this laser can be varied within wide limits according to the prior art by the use of dispersing elements in the laser resonator.
In the generation of coherent radiation in the wavelength range of approximately between 260 - 350 nm by frequency doubling of dye laser emission a particularly great conversion rate can be obtained in potassium dihydrogen phosphate crystals (KH.sub.2 PO.sub.4) and in ammonium dihydrogen phosphate crystals ((NH.sub.4) H.sub.2 PO.sub.4) which, abbreviated, are also termed KDP- and ADP-crystals. For obtaining a high field strength, the laser beam is focused into the crystal with a lens.
Investigations for frequency doubling of dye laser radiation in KDP- and ADP-crystals have shown that in a focused laser beam the phase adaption condition with irradiation by spectrally narrow-band laser radiation cannot be satisfied for the total aperture angle of the laser beam. See for instance J. Kuhl, H. Spitschan, Optics Communications 5, 382 (1972). The generation of the higher wave, therefore, can only be observed in a very narrow angular range. This leads to the fact that the cross-section of the generated UV-beam is strongly cut depending on the band width of the laser in the critical direction which is determined by the optical axis of the crystal.
As dispersing elements for tuning of the laser emission for instance, diffraction gratings, dispersion prisms, interference filters, Fabry-Perot etalons, achromatic lenses, Lyot-filters, or a combination of several such elements are used. The spectral tuning of the laser radiation in the case of the interference filter can, for instance, be obtained by a variation of the angular position of the filter relative to the direction of the beam. When using a Lyot-filter and Fabry-Perot etalon with a spacer of piezoelectric ceramics the transmission wavelength can be varied by a change in the electric voltage.
If a uniaxial double-refracting crystal is irradiated with the frequency-variable radiation of a dye laser in order to generate frequency-variable secondary radiation of double the frequency, then the condition of phase adaption in the crystal for the respectively irradiated laser frequency and its higher wave must be satisfied, since the refractive indices n.sub.o of the ordinary and n.sub.e of the extraordinary beam show dispersion in different manner. The problem of how to always re-establish the phase adaption in dependence on the variation of the wavelength can be solved, as is well-known, in two manners:
1. Crystal orientation is changed with the frequency by rotation of the crystal about the axis vertical to the optical crystal axis in such a manner that the angle between the direction of the laser beam in the crystal and the optical crystal axis just corresponds to the phase adaption angle for the respective frequency.
2. The crystal temperature and therewith the magnitude of the refractive indices n.sub.o and n.sub.e are changed with the frequency in such a manner that the respective relations (IV) and (V) remain satisfied.
Consequently, the spectral tuning of the secondary radiation generated in the crystal requires the simultaneous change of at least two experimental parameters:
Since the angular positions of the crystal and of the dispersing element in the laser resonator change in very different manner and respectively nonlinearly with the wavelength, a coupling of both movements according to the prior art is possible only after the involved dependence has been determined by the provision of a calibration curve. However, the use of a calibration curve requires a sufficient constancy of all experimental parameters, a condition which is not always assured. In particular the recording of a calibration curve is necessary for every new dispersing element which is combined with the crystal.